Polytope of Type {216,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {216,4}*1728d
if this polytope has a name.
Group : SmallGroup(1728,2203)
Rank : 3
Schlafli Type : {216,4}
Number of vertices, edges, etc : 216, 432, 4
Order of s0s1s2 : 216
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {108,4}*864b
3-fold quotients : {72,4}*576d
4-fold quotients : {54,4}*432b
6-fold quotients : {36,4}*288b
8-fold quotients : {27,4}*216
9-fold quotients : {24,4}*192d
12-fold quotients : {18,4}*144b
18-fold quotients : {12,4}*96b
24-fold quotients : {9,4}*72
36-fold quotients : {6,4}*48c
72-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 33)( 14, 34)( 15, 36)
( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)
( 24, 27)( 37,105)( 38,106)( 39,108)( 40,107)( 41,101)( 42,102)( 43,104)
( 44,103)( 45, 97)( 46, 98)( 47,100)( 48, 99)( 49, 93)( 50, 94)( 51, 96)
( 52, 95)( 53, 89)( 54, 90)( 55, 92)( 56, 91)( 57, 85)( 58, 86)( 59, 88)
( 60, 87)( 61, 81)( 62, 82)( 63, 84)( 64, 83)( 65, 77)( 66, 78)( 67, 80)
( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)(111,112)(113,117)(114,118)
(115,120)(116,119)(121,141)(122,142)(123,144)(124,143)(125,137)(126,138)
(127,140)(128,139)(129,133)(130,134)(131,136)(132,135)(145,213)(146,214)
(147,216)(148,215)(149,209)(150,210)(151,212)(152,211)(153,205)(154,206)
(155,208)(156,207)(157,201)(158,202)(159,204)(160,203)(161,197)(162,198)
(163,200)(164,199)(165,193)(166,194)(167,196)(168,195)(169,189)(170,190)
(171,192)(172,191)(173,185)(174,186)(175,188)(176,187)(177,181)(178,182)
(179,184)(180,183)(217,325)(218,326)(219,328)(220,327)(221,333)(222,334)
(223,336)(224,335)(225,329)(226,330)(227,332)(228,331)(229,357)(230,358)
(231,360)(232,359)(233,353)(234,354)(235,356)(236,355)(237,349)(238,350)
(239,352)(240,351)(241,345)(242,346)(243,348)(244,347)(245,341)(246,342)
(247,344)(248,343)(249,337)(250,338)(251,340)(252,339)(253,429)(254,430)
(255,432)(256,431)(257,425)(258,426)(259,428)(260,427)(261,421)(262,422)
(263,424)(264,423)(265,417)(266,418)(267,420)(268,419)(269,413)(270,414)
(271,416)(272,415)(273,409)(274,410)(275,412)(276,411)(277,405)(278,406)
(279,408)(280,407)(281,401)(282,402)(283,404)(284,403)(285,397)(286,398)
(287,400)(288,399)(289,393)(290,394)(291,396)(292,395)(293,389)(294,390)
(295,392)(296,391)(297,385)(298,386)(299,388)(300,387)(301,381)(302,382)
(303,384)(304,383)(305,377)(306,378)(307,380)(308,379)(309,373)(310,374)
(311,376)(312,375)(313,369)(314,370)(315,372)(316,371)(317,365)(318,366)
(319,368)(320,367)(321,361)(322,362)(323,364)(324,363)(433,649)(434,650)
(435,652)(436,651)(437,657)(438,658)(439,660)(440,659)(441,653)(442,654)
(443,656)(444,655)(445,681)(446,682)(447,684)(448,683)(449,677)(450,678)
(451,680)(452,679)(453,673)(454,674)(455,676)(456,675)(457,669)(458,670)
(459,672)(460,671)(461,665)(462,666)(463,668)(464,667)(465,661)(466,662)
(467,664)(468,663)(469,753)(470,754)(471,756)(472,755)(473,749)(474,750)
(475,752)(476,751)(477,745)(478,746)(479,748)(480,747)(481,741)(482,742)
(483,744)(484,743)(485,737)(486,738)(487,740)(488,739)(489,733)(490,734)
(491,736)(492,735)(493,729)(494,730)(495,732)(496,731)(497,725)(498,726)
(499,728)(500,727)(501,721)(502,722)(503,724)(504,723)(505,717)(506,718)
(507,720)(508,719)(509,713)(510,714)(511,716)(512,715)(513,709)(514,710)
(515,712)(516,711)(517,705)(518,706)(519,708)(520,707)(521,701)(522,702)
(523,704)(524,703)(525,697)(526,698)(527,700)(528,699)(529,693)(530,694)
(531,696)(532,695)(533,689)(534,690)(535,692)(536,691)(537,685)(538,686)
(539,688)(540,687)(541,757)(542,758)(543,760)(544,759)(545,765)(546,766)
(547,768)(548,767)(549,761)(550,762)(551,764)(552,763)(553,789)(554,790)
(555,792)(556,791)(557,785)(558,786)(559,788)(560,787)(561,781)(562,782)
(563,784)(564,783)(565,777)(566,778)(567,780)(568,779)(569,773)(570,774)
(571,776)(572,775)(573,769)(574,770)(575,772)(576,771)(577,861)(578,862)
(579,864)(580,863)(581,857)(582,858)(583,860)(584,859)(585,853)(586,854)
(587,856)(588,855)(589,849)(590,850)(591,852)(592,851)(593,845)(594,846)
(595,848)(596,847)(597,841)(598,842)(599,844)(600,843)(601,837)(602,838)
(603,840)(604,839)(605,833)(606,834)(607,836)(608,835)(609,829)(610,830)
(611,832)(612,831)(613,825)(614,826)(615,828)(616,827)(617,821)(618,822)
(619,824)(620,823)(621,817)(622,818)(623,820)(624,819)(625,813)(626,814)
(627,816)(628,815)(629,809)(630,810)(631,812)(632,811)(633,805)(634,806)
(635,808)(636,807)(637,801)(638,802)(639,804)(640,803)(641,797)(642,798)
(643,800)(644,799)(645,793)(646,794)(647,796)(648,795);;
s1 := ( 1,469)( 2,472)( 3,471)( 4,470)( 5,477)( 6,480)( 7,479)( 8,478)
( 9,473)( 10,476)( 11,475)( 12,474)( 13,501)( 14,504)( 15,503)( 16,502)
( 17,497)( 18,500)( 19,499)( 20,498)( 21,493)( 22,496)( 23,495)( 24,494)
( 25,489)( 26,492)( 27,491)( 28,490)( 29,485)( 30,488)( 31,487)( 32,486)
( 33,481)( 34,484)( 35,483)( 36,482)( 37,433)( 38,436)( 39,435)( 40,434)
( 41,441)( 42,444)( 43,443)( 44,442)( 45,437)( 46,440)( 47,439)( 48,438)
( 49,465)( 50,468)( 51,467)( 52,466)( 53,461)( 54,464)( 55,463)( 56,462)
( 57,457)( 58,460)( 59,459)( 60,458)( 61,453)( 62,456)( 63,455)( 64,454)
( 65,449)( 66,452)( 67,451)( 68,450)( 69,445)( 70,448)( 71,447)( 72,446)
( 73,537)( 74,540)( 75,539)( 76,538)( 77,533)( 78,536)( 79,535)( 80,534)
( 81,529)( 82,532)( 83,531)( 84,530)( 85,525)( 86,528)( 87,527)( 88,526)
( 89,521)( 90,524)( 91,523)( 92,522)( 93,517)( 94,520)( 95,519)( 96,518)
( 97,513)( 98,516)( 99,515)(100,514)(101,509)(102,512)(103,511)(104,510)
(105,505)(106,508)(107,507)(108,506)(109,577)(110,580)(111,579)(112,578)
(113,585)(114,588)(115,587)(116,586)(117,581)(118,584)(119,583)(120,582)
(121,609)(122,612)(123,611)(124,610)(125,605)(126,608)(127,607)(128,606)
(129,601)(130,604)(131,603)(132,602)(133,597)(134,600)(135,599)(136,598)
(137,593)(138,596)(139,595)(140,594)(141,589)(142,592)(143,591)(144,590)
(145,541)(146,544)(147,543)(148,542)(149,549)(150,552)(151,551)(152,550)
(153,545)(154,548)(155,547)(156,546)(157,573)(158,576)(159,575)(160,574)
(161,569)(162,572)(163,571)(164,570)(165,565)(166,568)(167,567)(168,566)
(169,561)(170,564)(171,563)(172,562)(173,557)(174,560)(175,559)(176,558)
(177,553)(178,556)(179,555)(180,554)(181,645)(182,648)(183,647)(184,646)
(185,641)(186,644)(187,643)(188,642)(189,637)(190,640)(191,639)(192,638)
(193,633)(194,636)(195,635)(196,634)(197,629)(198,632)(199,631)(200,630)
(201,625)(202,628)(203,627)(204,626)(205,621)(206,624)(207,623)(208,622)
(209,617)(210,620)(211,619)(212,618)(213,613)(214,616)(215,615)(216,614)
(217,793)(218,796)(219,795)(220,794)(221,801)(222,804)(223,803)(224,802)
(225,797)(226,800)(227,799)(228,798)(229,825)(230,828)(231,827)(232,826)
(233,821)(234,824)(235,823)(236,822)(237,817)(238,820)(239,819)(240,818)
(241,813)(242,816)(243,815)(244,814)(245,809)(246,812)(247,811)(248,810)
(249,805)(250,808)(251,807)(252,806)(253,757)(254,760)(255,759)(256,758)
(257,765)(258,768)(259,767)(260,766)(261,761)(262,764)(263,763)(264,762)
(265,789)(266,792)(267,791)(268,790)(269,785)(270,788)(271,787)(272,786)
(273,781)(274,784)(275,783)(276,782)(277,777)(278,780)(279,779)(280,778)
(281,773)(282,776)(283,775)(284,774)(285,769)(286,772)(287,771)(288,770)
(289,861)(290,864)(291,863)(292,862)(293,857)(294,860)(295,859)(296,858)
(297,853)(298,856)(299,855)(300,854)(301,849)(302,852)(303,851)(304,850)
(305,845)(306,848)(307,847)(308,846)(309,841)(310,844)(311,843)(312,842)
(313,837)(314,840)(315,839)(316,838)(317,833)(318,836)(319,835)(320,834)
(321,829)(322,832)(323,831)(324,830)(325,685)(326,688)(327,687)(328,686)
(329,693)(330,696)(331,695)(332,694)(333,689)(334,692)(335,691)(336,690)
(337,717)(338,720)(339,719)(340,718)(341,713)(342,716)(343,715)(344,714)
(345,709)(346,712)(347,711)(348,710)(349,705)(350,708)(351,707)(352,706)
(353,701)(354,704)(355,703)(356,702)(357,697)(358,700)(359,699)(360,698)
(361,649)(362,652)(363,651)(364,650)(365,657)(366,660)(367,659)(368,658)
(369,653)(370,656)(371,655)(372,654)(373,681)(374,684)(375,683)(376,682)
(377,677)(378,680)(379,679)(380,678)(381,673)(382,676)(383,675)(384,674)
(385,669)(386,672)(387,671)(388,670)(389,665)(390,668)(391,667)(392,666)
(393,661)(394,664)(395,663)(396,662)(397,753)(398,756)(399,755)(400,754)
(401,749)(402,752)(403,751)(404,750)(405,745)(406,748)(407,747)(408,746)
(409,741)(410,744)(411,743)(412,742)(413,737)(414,740)(415,739)(416,738)
(417,733)(418,736)(419,735)(420,734)(421,729)(422,732)(423,731)(424,730)
(425,725)(426,728)(427,727)(428,726)(429,721)(430,724)(431,723)(432,722);;
s2 := ( 1,110)( 2,109)( 3,112)( 4,111)( 5,114)( 6,113)( 7,116)( 8,115)
( 9,118)( 10,117)( 11,120)( 12,119)( 13,122)( 14,121)( 15,124)( 16,123)
( 17,126)( 18,125)( 19,128)( 20,127)( 21,130)( 22,129)( 23,132)( 24,131)
( 25,134)( 26,133)( 27,136)( 28,135)( 29,138)( 30,137)( 31,140)( 32,139)
( 33,142)( 34,141)( 35,144)( 36,143)( 37,146)( 38,145)( 39,148)( 40,147)
( 41,150)( 42,149)( 43,152)( 44,151)( 45,154)( 46,153)( 47,156)( 48,155)
( 49,158)( 50,157)( 51,160)( 52,159)( 53,162)( 54,161)( 55,164)( 56,163)
( 57,166)( 58,165)( 59,168)( 60,167)( 61,170)( 62,169)( 63,172)( 64,171)
( 65,174)( 66,173)( 67,176)( 68,175)( 69,178)( 70,177)( 71,180)( 72,179)
( 73,182)( 74,181)( 75,184)( 76,183)( 77,186)( 78,185)( 79,188)( 80,187)
( 81,190)( 82,189)( 83,192)( 84,191)( 85,194)( 86,193)( 87,196)( 88,195)
( 89,198)( 90,197)( 91,200)( 92,199)( 93,202)( 94,201)( 95,204)( 96,203)
( 97,206)( 98,205)( 99,208)(100,207)(101,210)(102,209)(103,212)(104,211)
(105,214)(106,213)(107,216)(108,215)(217,326)(218,325)(219,328)(220,327)
(221,330)(222,329)(223,332)(224,331)(225,334)(226,333)(227,336)(228,335)
(229,338)(230,337)(231,340)(232,339)(233,342)(234,341)(235,344)(236,343)
(237,346)(238,345)(239,348)(240,347)(241,350)(242,349)(243,352)(244,351)
(245,354)(246,353)(247,356)(248,355)(249,358)(250,357)(251,360)(252,359)
(253,362)(254,361)(255,364)(256,363)(257,366)(258,365)(259,368)(260,367)
(261,370)(262,369)(263,372)(264,371)(265,374)(266,373)(267,376)(268,375)
(269,378)(270,377)(271,380)(272,379)(273,382)(274,381)(275,384)(276,383)
(277,386)(278,385)(279,388)(280,387)(281,390)(282,389)(283,392)(284,391)
(285,394)(286,393)(287,396)(288,395)(289,398)(290,397)(291,400)(292,399)
(293,402)(294,401)(295,404)(296,403)(297,406)(298,405)(299,408)(300,407)
(301,410)(302,409)(303,412)(304,411)(305,414)(306,413)(307,416)(308,415)
(309,418)(310,417)(311,420)(312,419)(313,422)(314,421)(315,424)(316,423)
(317,426)(318,425)(319,428)(320,427)(321,430)(322,429)(323,432)(324,431)
(433,542)(434,541)(435,544)(436,543)(437,546)(438,545)(439,548)(440,547)
(441,550)(442,549)(443,552)(444,551)(445,554)(446,553)(447,556)(448,555)
(449,558)(450,557)(451,560)(452,559)(453,562)(454,561)(455,564)(456,563)
(457,566)(458,565)(459,568)(460,567)(461,570)(462,569)(463,572)(464,571)
(465,574)(466,573)(467,576)(468,575)(469,578)(470,577)(471,580)(472,579)
(473,582)(474,581)(475,584)(476,583)(477,586)(478,585)(479,588)(480,587)
(481,590)(482,589)(483,592)(484,591)(485,594)(486,593)(487,596)(488,595)
(489,598)(490,597)(491,600)(492,599)(493,602)(494,601)(495,604)(496,603)
(497,606)(498,605)(499,608)(500,607)(501,610)(502,609)(503,612)(504,611)
(505,614)(506,613)(507,616)(508,615)(509,618)(510,617)(511,620)(512,619)
(513,622)(514,621)(515,624)(516,623)(517,626)(518,625)(519,628)(520,627)
(521,630)(522,629)(523,632)(524,631)(525,634)(526,633)(527,636)(528,635)
(529,638)(530,637)(531,640)(532,639)(533,642)(534,641)(535,644)(536,643)
(537,646)(538,645)(539,648)(540,647)(649,758)(650,757)(651,760)(652,759)
(653,762)(654,761)(655,764)(656,763)(657,766)(658,765)(659,768)(660,767)
(661,770)(662,769)(663,772)(664,771)(665,774)(666,773)(667,776)(668,775)
(669,778)(670,777)(671,780)(672,779)(673,782)(674,781)(675,784)(676,783)
(677,786)(678,785)(679,788)(680,787)(681,790)(682,789)(683,792)(684,791)
(685,794)(686,793)(687,796)(688,795)(689,798)(690,797)(691,800)(692,799)
(693,802)(694,801)(695,804)(696,803)(697,806)(698,805)(699,808)(700,807)
(701,810)(702,809)(703,812)(704,811)(705,814)(706,813)(707,816)(708,815)
(709,818)(710,817)(711,820)(712,819)(713,822)(714,821)(715,824)(716,823)
(717,826)(718,825)(719,828)(720,827)(721,830)(722,829)(723,832)(724,831)
(725,834)(726,833)(727,836)(728,835)(729,838)(730,837)(731,840)(732,839)
(733,842)(734,841)(735,844)(736,843)(737,846)(738,845)(739,848)(740,847)
(741,850)(742,849)(743,852)(744,851)(745,854)(746,853)(747,856)(748,855)
(749,858)(750,857)(751,860)(752,859)(753,862)(754,861)(755,864)(756,863);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(864)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 33)( 14, 34)
( 15, 36)( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)
( 23, 28)( 24, 27)( 37,105)( 38,106)( 39,108)( 40,107)( 41,101)( 42,102)
( 43,104)( 44,103)( 45, 97)( 46, 98)( 47,100)( 48, 99)( 49, 93)( 50, 94)
( 51, 96)( 52, 95)( 53, 89)( 54, 90)( 55, 92)( 56, 91)( 57, 85)( 58, 86)
( 59, 88)( 60, 87)( 61, 81)( 62, 82)( 63, 84)( 64, 83)( 65, 77)( 66, 78)
( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)(111,112)(113,117)
(114,118)(115,120)(116,119)(121,141)(122,142)(123,144)(124,143)(125,137)
(126,138)(127,140)(128,139)(129,133)(130,134)(131,136)(132,135)(145,213)
(146,214)(147,216)(148,215)(149,209)(150,210)(151,212)(152,211)(153,205)
(154,206)(155,208)(156,207)(157,201)(158,202)(159,204)(160,203)(161,197)
(162,198)(163,200)(164,199)(165,193)(166,194)(167,196)(168,195)(169,189)
(170,190)(171,192)(172,191)(173,185)(174,186)(175,188)(176,187)(177,181)
(178,182)(179,184)(180,183)(217,325)(218,326)(219,328)(220,327)(221,333)
(222,334)(223,336)(224,335)(225,329)(226,330)(227,332)(228,331)(229,357)
(230,358)(231,360)(232,359)(233,353)(234,354)(235,356)(236,355)(237,349)
(238,350)(239,352)(240,351)(241,345)(242,346)(243,348)(244,347)(245,341)
(246,342)(247,344)(248,343)(249,337)(250,338)(251,340)(252,339)(253,429)
(254,430)(255,432)(256,431)(257,425)(258,426)(259,428)(260,427)(261,421)
(262,422)(263,424)(264,423)(265,417)(266,418)(267,420)(268,419)(269,413)
(270,414)(271,416)(272,415)(273,409)(274,410)(275,412)(276,411)(277,405)
(278,406)(279,408)(280,407)(281,401)(282,402)(283,404)(284,403)(285,397)
(286,398)(287,400)(288,399)(289,393)(290,394)(291,396)(292,395)(293,389)
(294,390)(295,392)(296,391)(297,385)(298,386)(299,388)(300,387)(301,381)
(302,382)(303,384)(304,383)(305,377)(306,378)(307,380)(308,379)(309,373)
(310,374)(311,376)(312,375)(313,369)(314,370)(315,372)(316,371)(317,365)
(318,366)(319,368)(320,367)(321,361)(322,362)(323,364)(324,363)(433,649)
(434,650)(435,652)(436,651)(437,657)(438,658)(439,660)(440,659)(441,653)
(442,654)(443,656)(444,655)(445,681)(446,682)(447,684)(448,683)(449,677)
(450,678)(451,680)(452,679)(453,673)(454,674)(455,676)(456,675)(457,669)
(458,670)(459,672)(460,671)(461,665)(462,666)(463,668)(464,667)(465,661)
(466,662)(467,664)(468,663)(469,753)(470,754)(471,756)(472,755)(473,749)
(474,750)(475,752)(476,751)(477,745)(478,746)(479,748)(480,747)(481,741)
(482,742)(483,744)(484,743)(485,737)(486,738)(487,740)(488,739)(489,733)
(490,734)(491,736)(492,735)(493,729)(494,730)(495,732)(496,731)(497,725)
(498,726)(499,728)(500,727)(501,721)(502,722)(503,724)(504,723)(505,717)
(506,718)(507,720)(508,719)(509,713)(510,714)(511,716)(512,715)(513,709)
(514,710)(515,712)(516,711)(517,705)(518,706)(519,708)(520,707)(521,701)
(522,702)(523,704)(524,703)(525,697)(526,698)(527,700)(528,699)(529,693)
(530,694)(531,696)(532,695)(533,689)(534,690)(535,692)(536,691)(537,685)
(538,686)(539,688)(540,687)(541,757)(542,758)(543,760)(544,759)(545,765)
(546,766)(547,768)(548,767)(549,761)(550,762)(551,764)(552,763)(553,789)
(554,790)(555,792)(556,791)(557,785)(558,786)(559,788)(560,787)(561,781)
(562,782)(563,784)(564,783)(565,777)(566,778)(567,780)(568,779)(569,773)
(570,774)(571,776)(572,775)(573,769)(574,770)(575,772)(576,771)(577,861)
(578,862)(579,864)(580,863)(581,857)(582,858)(583,860)(584,859)(585,853)
(586,854)(587,856)(588,855)(589,849)(590,850)(591,852)(592,851)(593,845)
(594,846)(595,848)(596,847)(597,841)(598,842)(599,844)(600,843)(601,837)
(602,838)(603,840)(604,839)(605,833)(606,834)(607,836)(608,835)(609,829)
(610,830)(611,832)(612,831)(613,825)(614,826)(615,828)(616,827)(617,821)
(618,822)(619,824)(620,823)(621,817)(622,818)(623,820)(624,819)(625,813)
(626,814)(627,816)(628,815)(629,809)(630,810)(631,812)(632,811)(633,805)
(634,806)(635,808)(636,807)(637,801)(638,802)(639,804)(640,803)(641,797)
(642,798)(643,800)(644,799)(645,793)(646,794)(647,796)(648,795);
s1 := Sym(864)!( 1,469)( 2,472)( 3,471)( 4,470)( 5,477)( 6,480)( 7,479)
( 8,478)( 9,473)( 10,476)( 11,475)( 12,474)( 13,501)( 14,504)( 15,503)
( 16,502)( 17,497)( 18,500)( 19,499)( 20,498)( 21,493)( 22,496)( 23,495)
( 24,494)( 25,489)( 26,492)( 27,491)( 28,490)( 29,485)( 30,488)( 31,487)
( 32,486)( 33,481)( 34,484)( 35,483)( 36,482)( 37,433)( 38,436)( 39,435)
( 40,434)( 41,441)( 42,444)( 43,443)( 44,442)( 45,437)( 46,440)( 47,439)
( 48,438)( 49,465)( 50,468)( 51,467)( 52,466)( 53,461)( 54,464)( 55,463)
( 56,462)( 57,457)( 58,460)( 59,459)( 60,458)( 61,453)( 62,456)( 63,455)
( 64,454)( 65,449)( 66,452)( 67,451)( 68,450)( 69,445)( 70,448)( 71,447)
( 72,446)( 73,537)( 74,540)( 75,539)( 76,538)( 77,533)( 78,536)( 79,535)
( 80,534)( 81,529)( 82,532)( 83,531)( 84,530)( 85,525)( 86,528)( 87,527)
( 88,526)( 89,521)( 90,524)( 91,523)( 92,522)( 93,517)( 94,520)( 95,519)
( 96,518)( 97,513)( 98,516)( 99,515)(100,514)(101,509)(102,512)(103,511)
(104,510)(105,505)(106,508)(107,507)(108,506)(109,577)(110,580)(111,579)
(112,578)(113,585)(114,588)(115,587)(116,586)(117,581)(118,584)(119,583)
(120,582)(121,609)(122,612)(123,611)(124,610)(125,605)(126,608)(127,607)
(128,606)(129,601)(130,604)(131,603)(132,602)(133,597)(134,600)(135,599)
(136,598)(137,593)(138,596)(139,595)(140,594)(141,589)(142,592)(143,591)
(144,590)(145,541)(146,544)(147,543)(148,542)(149,549)(150,552)(151,551)
(152,550)(153,545)(154,548)(155,547)(156,546)(157,573)(158,576)(159,575)
(160,574)(161,569)(162,572)(163,571)(164,570)(165,565)(166,568)(167,567)
(168,566)(169,561)(170,564)(171,563)(172,562)(173,557)(174,560)(175,559)
(176,558)(177,553)(178,556)(179,555)(180,554)(181,645)(182,648)(183,647)
(184,646)(185,641)(186,644)(187,643)(188,642)(189,637)(190,640)(191,639)
(192,638)(193,633)(194,636)(195,635)(196,634)(197,629)(198,632)(199,631)
(200,630)(201,625)(202,628)(203,627)(204,626)(205,621)(206,624)(207,623)
(208,622)(209,617)(210,620)(211,619)(212,618)(213,613)(214,616)(215,615)
(216,614)(217,793)(218,796)(219,795)(220,794)(221,801)(222,804)(223,803)
(224,802)(225,797)(226,800)(227,799)(228,798)(229,825)(230,828)(231,827)
(232,826)(233,821)(234,824)(235,823)(236,822)(237,817)(238,820)(239,819)
(240,818)(241,813)(242,816)(243,815)(244,814)(245,809)(246,812)(247,811)
(248,810)(249,805)(250,808)(251,807)(252,806)(253,757)(254,760)(255,759)
(256,758)(257,765)(258,768)(259,767)(260,766)(261,761)(262,764)(263,763)
(264,762)(265,789)(266,792)(267,791)(268,790)(269,785)(270,788)(271,787)
(272,786)(273,781)(274,784)(275,783)(276,782)(277,777)(278,780)(279,779)
(280,778)(281,773)(282,776)(283,775)(284,774)(285,769)(286,772)(287,771)
(288,770)(289,861)(290,864)(291,863)(292,862)(293,857)(294,860)(295,859)
(296,858)(297,853)(298,856)(299,855)(300,854)(301,849)(302,852)(303,851)
(304,850)(305,845)(306,848)(307,847)(308,846)(309,841)(310,844)(311,843)
(312,842)(313,837)(314,840)(315,839)(316,838)(317,833)(318,836)(319,835)
(320,834)(321,829)(322,832)(323,831)(324,830)(325,685)(326,688)(327,687)
(328,686)(329,693)(330,696)(331,695)(332,694)(333,689)(334,692)(335,691)
(336,690)(337,717)(338,720)(339,719)(340,718)(341,713)(342,716)(343,715)
(344,714)(345,709)(346,712)(347,711)(348,710)(349,705)(350,708)(351,707)
(352,706)(353,701)(354,704)(355,703)(356,702)(357,697)(358,700)(359,699)
(360,698)(361,649)(362,652)(363,651)(364,650)(365,657)(366,660)(367,659)
(368,658)(369,653)(370,656)(371,655)(372,654)(373,681)(374,684)(375,683)
(376,682)(377,677)(378,680)(379,679)(380,678)(381,673)(382,676)(383,675)
(384,674)(385,669)(386,672)(387,671)(388,670)(389,665)(390,668)(391,667)
(392,666)(393,661)(394,664)(395,663)(396,662)(397,753)(398,756)(399,755)
(400,754)(401,749)(402,752)(403,751)(404,750)(405,745)(406,748)(407,747)
(408,746)(409,741)(410,744)(411,743)(412,742)(413,737)(414,740)(415,739)
(416,738)(417,733)(418,736)(419,735)(420,734)(421,729)(422,732)(423,731)
(424,730)(425,725)(426,728)(427,727)(428,726)(429,721)(430,724)(431,723)
(432,722);
s2 := Sym(864)!( 1,110)( 2,109)( 3,112)( 4,111)( 5,114)( 6,113)( 7,116)
( 8,115)( 9,118)( 10,117)( 11,120)( 12,119)( 13,122)( 14,121)( 15,124)
( 16,123)( 17,126)( 18,125)( 19,128)( 20,127)( 21,130)( 22,129)( 23,132)
( 24,131)( 25,134)( 26,133)( 27,136)( 28,135)( 29,138)( 30,137)( 31,140)
( 32,139)( 33,142)( 34,141)( 35,144)( 36,143)( 37,146)( 38,145)( 39,148)
( 40,147)( 41,150)( 42,149)( 43,152)( 44,151)( 45,154)( 46,153)( 47,156)
( 48,155)( 49,158)( 50,157)( 51,160)( 52,159)( 53,162)( 54,161)( 55,164)
( 56,163)( 57,166)( 58,165)( 59,168)( 60,167)( 61,170)( 62,169)( 63,172)
( 64,171)( 65,174)( 66,173)( 67,176)( 68,175)( 69,178)( 70,177)( 71,180)
( 72,179)( 73,182)( 74,181)( 75,184)( 76,183)( 77,186)( 78,185)( 79,188)
( 80,187)( 81,190)( 82,189)( 83,192)( 84,191)( 85,194)( 86,193)( 87,196)
( 88,195)( 89,198)( 90,197)( 91,200)( 92,199)( 93,202)( 94,201)( 95,204)
( 96,203)( 97,206)( 98,205)( 99,208)(100,207)(101,210)(102,209)(103,212)
(104,211)(105,214)(106,213)(107,216)(108,215)(217,326)(218,325)(219,328)
(220,327)(221,330)(222,329)(223,332)(224,331)(225,334)(226,333)(227,336)
(228,335)(229,338)(230,337)(231,340)(232,339)(233,342)(234,341)(235,344)
(236,343)(237,346)(238,345)(239,348)(240,347)(241,350)(242,349)(243,352)
(244,351)(245,354)(246,353)(247,356)(248,355)(249,358)(250,357)(251,360)
(252,359)(253,362)(254,361)(255,364)(256,363)(257,366)(258,365)(259,368)
(260,367)(261,370)(262,369)(263,372)(264,371)(265,374)(266,373)(267,376)
(268,375)(269,378)(270,377)(271,380)(272,379)(273,382)(274,381)(275,384)
(276,383)(277,386)(278,385)(279,388)(280,387)(281,390)(282,389)(283,392)
(284,391)(285,394)(286,393)(287,396)(288,395)(289,398)(290,397)(291,400)
(292,399)(293,402)(294,401)(295,404)(296,403)(297,406)(298,405)(299,408)
(300,407)(301,410)(302,409)(303,412)(304,411)(305,414)(306,413)(307,416)
(308,415)(309,418)(310,417)(311,420)(312,419)(313,422)(314,421)(315,424)
(316,423)(317,426)(318,425)(319,428)(320,427)(321,430)(322,429)(323,432)
(324,431)(433,542)(434,541)(435,544)(436,543)(437,546)(438,545)(439,548)
(440,547)(441,550)(442,549)(443,552)(444,551)(445,554)(446,553)(447,556)
(448,555)(449,558)(450,557)(451,560)(452,559)(453,562)(454,561)(455,564)
(456,563)(457,566)(458,565)(459,568)(460,567)(461,570)(462,569)(463,572)
(464,571)(465,574)(466,573)(467,576)(468,575)(469,578)(470,577)(471,580)
(472,579)(473,582)(474,581)(475,584)(476,583)(477,586)(478,585)(479,588)
(480,587)(481,590)(482,589)(483,592)(484,591)(485,594)(486,593)(487,596)
(488,595)(489,598)(490,597)(491,600)(492,599)(493,602)(494,601)(495,604)
(496,603)(497,606)(498,605)(499,608)(500,607)(501,610)(502,609)(503,612)
(504,611)(505,614)(506,613)(507,616)(508,615)(509,618)(510,617)(511,620)
(512,619)(513,622)(514,621)(515,624)(516,623)(517,626)(518,625)(519,628)
(520,627)(521,630)(522,629)(523,632)(524,631)(525,634)(526,633)(527,636)
(528,635)(529,638)(530,637)(531,640)(532,639)(533,642)(534,641)(535,644)
(536,643)(537,646)(538,645)(539,648)(540,647)(649,758)(650,757)(651,760)
(652,759)(653,762)(654,761)(655,764)(656,763)(657,766)(658,765)(659,768)
(660,767)(661,770)(662,769)(663,772)(664,771)(665,774)(666,773)(667,776)
(668,775)(669,778)(670,777)(671,780)(672,779)(673,782)(674,781)(675,784)
(676,783)(677,786)(678,785)(679,788)(680,787)(681,790)(682,789)(683,792)
(684,791)(685,794)(686,793)(687,796)(688,795)(689,798)(690,797)(691,800)
(692,799)(693,802)(694,801)(695,804)(696,803)(697,806)(698,805)(699,808)
(700,807)(701,810)(702,809)(703,812)(704,811)(705,814)(706,813)(707,816)
(708,815)(709,818)(710,817)(711,820)(712,819)(713,822)(714,821)(715,824)
(716,823)(717,826)(718,825)(719,828)(720,827)(721,830)(722,829)(723,832)
(724,831)(725,834)(726,833)(727,836)(728,835)(729,838)(730,837)(731,840)
(732,839)(733,842)(734,841)(735,844)(736,843)(737,846)(738,845)(739,848)
(740,847)(741,850)(742,849)(743,852)(744,851)(745,854)(746,853)(747,856)
(748,855)(749,858)(750,857)(751,860)(752,859)(753,862)(754,861)(755,864)
(756,863);
poly := sub<Sym(864)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope